International Journal of Theoretical Physics

, Volume 46, Issue 11, pp 2887–2900 | Cite as

An Intrinsic Topology for Orthomodular Lattices

  • Olivier Brunet


We present a general way to define a topology on orthomodular lattices. We show that in the case of a Hilbert lattice, this topology is equivalent to that induced by the metrics of the corresponding Hilbert space. Moreover, we show that in the case of a boolean algebra, the obtained topology is the discrete one. Thus, our construction provides a general tool for studying orthomodular lattices but also a way to distinguish classical and quantum logics.


Hilbert Space Modal Logic Boolean Algebra Closed Subspace Quantum Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Leibniz-IMAG LaboratoryGrenobleFrance

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